SubsidieMeestersSymmetry and Optimization at the Frontiers of Computation
This project aims to establish noncommutative group optimization foundations to solve complex problems across various fields, enhancing algorithms and quantum computing applications.
Projectdetails
Introduction
Noncommutative group optimization is a powerful emerging paradigm, which has already led to the solution of outstanding problems in computational complexity, algebra, and statistics. Pioneered by the PI and collaborators, it generalizes convex optimization from Euclidean space to the far more general setting of curved spaces with symmetries.
Significance of Noncommutative Group Optimization
Its unfamiliar kind of convexity has recently received much attention in statistics and machine learning. The symmetries are realized by noncommutative groups and imply a high degree of algebraic structure. This combination of symmetry and optimization promises to be key to fast algorithms and deep structural insight.
Interdisciplinary Connections
Noncommutative group optimization connects important problems across a wide range of disciplines that appear unrelated at first glance:
- Program testing and derandomization in computer science
- Estimation problems in statistics
- Isomorphism problems in algebra
- The P vs NP problem and circuit lower bounds in complexity theory
- Optimal transport in machine learning
- Marginal and entanglement problems in quantum information
- Optimization on quantum computers
This list contains both discrete and continuous problems, theoretical and applied ones, for classical as well as for quantum computers. They have been studied separately over many years by many authors. Here they are brought together in a new innovative way.
Project Goals
This project aims to develop the theoretical and algorithmic foundations of noncommutative group optimization and apply it to longstanding theoretical problems and practical applications.
Expected Impact
This has high potential for long-lasting impact at several frontiers of computation:
- In addition to contributing a new paradigm and widely-applicable methods to optimization,
- We aim to give efficient algorithmic solutions to difficult problems in algebra,
- Make progress on the limits of efficient computation, and
- Unlock the potential of quantum computers for optimization.
Financiële details & Tijdlijn
Financiële details
| Subsidiebedrag | € 1.500.000 |
| Totale projectbegroting | € 1.500.000 |
Tijdlijn
| Startdatum | 1-5-2022 |
| Einddatum | 30-4-2027 |
| Subsidiejaar | 2022 |
Partners & Locaties
Projectpartners
- RUHR-UNIVERSITAET BOCHUMpenvoerder
Land(en)
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This project aims to enhance post-quantum cryptography by leveraging algebraic groups to improve security proofs and develop advanced cryptosystems through modern arithmetic techniques.
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This project aims to advance projection-free optimization methods to match the efficiency of projection-based techniques, enhancing continuous optimization for complex, structured constraints in data science and AI.
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